The Goodison Park chief, who has now secured three European qualifications in four seasons, said: "We deserved it. We have been in the top five since new year, and our form has been coming back in recent games."
Moyes said: "We finished on a good note, with a good performance. All we lacked in the first half was the finish to underline our superiority at that stage.
"But I don't feel that we showed any nerves. We passed the ball well, and produced a really, really good performance. There was character and confidence.
"I wanted to win, I wanted 65 points. In many other seasons, that would have got us into the Champions League. When we did achieve that a couple of years ago, we did it with 61 points.
"This is one of my most pleasing seasons at the club, but I always prefer to think that the most pleasing season is still to come."